Category: Relation and Functions

Question Number 67034 by mathmax by abdo last updated on 22/Aug/19 $$calculate\sum _{n=1}^{\mathrm{\infty }}\frac{cos\left(2nx\right)}{n}$$ Commented by mathmax by abdo last updated on 23/Aug/19…

Question Number 67023 by mathmax by abdo last updated on 21/Aug/19 $$findthesequence{U}_{n}wichverify{U}_n+U_{n+1}=sin\left(n\right)\mathrm{\forall }nfromn$$ Commented by mathmax by abdo last updated on…

Question Number 67015 by mathmax by abdo last updated on 21/Aug/19 $$letf\left(x\right)=arctan(1+e^{-\sqrt{1+x^2}})$$$$calculate{f}^{{}^{\prime }}\left(x\right)and{f}^{{}^{″}}\left(x\right).$$$$1)find{lim}_{x\to +\mathrm{\infty }}f\left(x\right)and{lim}_{x\to -\mathrm{\infty }}f\left(x\right)$$$$\left.\mathrm{3}\right){study}\:{the}\:{variation}\:{of}\:{f}\left({x}\right) \…

Question Number 67013 by mathmax by abdo last updated on 21/Aug/19 $$findthevalueof\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^n}{(n+1)n^3}$$ Commented by mathmax by abdo last updated…

Question Number 66937 by Cmr 237 last updated on 20/Aug/19 Answered by mr W last updated on 21/Aug/19 $$lett={81}^{{\sin }^{2}x}$$$$\mathrm{81}^{\mathrm{cos}^{\mathrm{2}} \:{x}} =\mathrm{81}^{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \:{x}}…